Problem: Solve for $x$ and $y$ using substitution. ${-2x+5y = -1}$ ${x = 5y+8}$
Solution: Since $x$ has already been solved for, substitute $5y+8$ for $x$ in the first equation. ${-2}{(5y+8)}{+ 5y = -1}$ Simplify and solve for $y$ $-10y-16 + 5y = -1$ $-5y-16 = -1$ $-5y-16{+16} = -1{+16}$ $-5y = 15$ $\dfrac{-5y}{{-5}} = \dfrac{15}{{-5}}$ ${y = -3}$ Now that you know ${y = -3}$ , plug it back into $\thinspace {x = 5y+8}\thinspace$ to find $x$ ${x = 5}{(-3)}{ + 8}$ $x = -15 + 8$ ${x = -7}$ You can also plug ${y = -3}$ into $\thinspace {-2x+5y = -1}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(-3)}{= -1}$ ${x = -7}$